Question

Cum se rezolva exercitiul din poza?

Answer 1

a+b=$\frac{1}{ \sqrt{5}+2 }+ \frac{1}{3+ \sqrt{8} }+ \frac{1}{ \sqrt{5}-2 }+ \frac{1}{3-\sqrt{8}}$
Prima fractie o amplificam cu √5-2 ,a doua cu 3-√8, a treia cu √5+2 iar ultima cu 3+√8 ⇒
⇒$= \frac{ \sqrt{5}-2 }{5-4}+ \frac{3- \sqrt{8} }{9-8}+ \frac{ \sqrt{5}+2 }{5-4}+ \frac{3+ \sqrt{8} }{9-8}= \sqrt{5}-2+3- \sqrt{8}+ \sqrt{5} +2+3+ \sqrt{8}$
=2√5+6